BROOKSVILLE — Beginning this week, students across Florida will be tested on the most rigorous math standards the state has ever seen.
Hernando school officials say they are ready. The standards on the new Florida Comprehensive Assessment Test may be tougher, but they've been a long time coming.
In the past, students learned the procedures but missed out on the conceptual knowledge, said Moton Elementary School math coach Sabrena Klausman.
With the new standards, which took effect this year, fewer concepts are taught, but the level of understanding required for mastery has greatly increased.
It's a change so significant, it has required a whole new way of teaching to go along with it.
"We could not continue to deliver math instruction the way we were doing it," said Marcia Austin, Hernando County schools math supervisor. "Math instruction had become too structured and too skill-based."
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On a recent morning at Moton Elementary, teacher Gale Reed told her third-graders they would work on three activities, all with the ultimate goal of answering some of the big questions they'd been wrestling with all week.
"How can we use squares and triangles to find the area?" she asked, before upping the ante.
"Can different shapes have the same area? How can you prove this? And how can we find the area of a partially covered shape?"
Under the new standards, students are taught multiple ways to reach answers. Getting the right answer matters, but the path is up to them.
After a vocabulary review, students got to work with partners. As Reed orbited the room, she prodded them to talk about the thinking behind their solutions.
Many students counted the squares to find the area of several shapes, which yielded the correct answer. But partners Nolan Fry and Matt Platt found a shortcut, multiplying the two sides to find the area.
"When you present, be sure and tell (your classmates) what you did," Reed said. "That's a really good tip."
Madie Walsh told the class about the rectangle she created out of "turtle steps." Her rectangle had two sides with 70 steps and two with 30. She, too, found a shortcut to the correct answer of 200.
"We took away the zeros and made sure all the numbers added to 20," she said.
Reed smiled. She danced. She asked Madie to explain how she got her answer.
"I added 3 plus 3 plus 7 plus 7 and it equals 20," Madie said. "I didn't need to add to 200."
It would have been easier for Mrs. Reed to teach such tricks to the entire class. But she instinctively knew something about cognitive science that is now supported by the new Florida standards. When you discover a solution for yourself, you remember it.
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Researchers say understanding how numbers work is far more important than spitting out a quick answer based on a memorized formula.
"In my day, you had to do things in your head," said Keith Devlin, a Stanford mathematics professor who moonlights as National Public Radio's "Math Guy." "Today, I have a calculator on my cell phone. All of us have calculations provided for us — it's quicker and more accurate."
But what we need to know and be able to do is more complex, Devlin said. A spreadsheet can perform the calculations, but it's useless without the proper formula. Suddenly, algebra is critical.
"You have to know what the computer is doing," Devlin said. "You have to learn arithmetic, but the learning has to be different, it's not procedural."
It was a hard lesson for Florida policymakers. When the conservative Thomas B. Fordham Institute issued a State of States Standards report in 2006, it gave Florida an "F" in math.
The following year, the Florida Department of Education reworked its curriculum standards, taking note of the National Council of Teachers of Mathematics' advice to teach fewer concepts more intensively.
By 2010, Fordham had awarded Florida's math program an "A," and the state found itself in perfect alignment with new National Common Core Standards needed to qualify for federal Race to the Top stimulus funds.
Where Florida was once viewed as an underachiever, experts say it is now on track to narrow the gap between U.S. students and their international peers.
"These standards are very focused, coherent, rigorous and demanding," said William Schmidt, a professor at Michigan State University who participated in the international benchmarking effort.
"We've come a long way from 'every teacher can do what they want' in math. In the past, people taught things because they were in the book or they liked to teach it. But the curriculum didn't reflect the internal logical structure of mathematics. Now, we have a road map."
It's a road map officials in Hernando have used to standardize their own math program. In the past, each school chose its own approach.
Now each elementary school in the county is using a single, state-approved program called enVisionMATH.
Students needed more hands-on, problem-based instruction, said Austin, the math supervisor, who served on the state selection committee and also facilitated the textbook selection process in Hernando.
"What teachers teach is really based on students," she said. "However, we have a destination, and that's the FCAT."
Success on the new FCAT can't be assessed until the state has several years' worth of data to compare, but local educators are seeing promising trends with the new standards.
With the new program in place, Klausman, the Moton math coach, has even seen the latest crop of kindergarteners demonstrate an understanding of basic algebra.
The changes can come as a shock to parents, who expect to be able to assist school-age children with homework. Moton and other elementary schools have held parent nights to explain the philosophy behind the program.
Parent Debra LeGrand said it's a far cry from the sink-or-swim approach she learned in elementary math.
"Back then, teachers would say, 'You're all going to have to get it this way and this is how,' " LeGrand said. "And if you didn't get it, you didn't get it."
These days, her first- and third-grade daughters at Moton are encouraged to seek out creative solutions. There's no "right" way to solve a problem.
LeGrand said they're learning a lot and doing well. But the real payoff is even bigger.
Her kids love math.
Shary Lyssy Marshall can be reached at firstname.lastname@example.org.